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Oh, I see.
I'm still not sure what that has to do with my "inf * 0 = 0" comment though?

Yes, 2(inf) will grow twice as fast as 1(inf), but they'll both keep going forever.

Well it's been a while since I've done that kind of math, but now that I think of it, yes that's what I meant. ;)

But putting all the math stuff aside for a second - aren't 0 and infinity exact...

Well using that logic: if x/0 = infinity and 0/x = 0 then


x * 0 = 0
0 x
because then the x's and 0's would cancel each other out and you'd be left with 0.

Yeah, I remember my teachers always saying that x/0 is undefined, not infinity; but why is infinity * 0 undefined?

Shouldn't those both equal 0? Anything times 0 equals 0 right?

OK, let me start over... The number I was talking about with (0.000...1) is not a quantifiable amount. Maybe if I said (1/infinity) my point would be more clear, although after all this I think I...

There are an infinite number of numbers, regardless of whether they're natural, whole, integer, rational or irrational numbers, so I'm not sure what your point is?
If you could count forever, then...

I know you can't write a 1 on the end on paper, but I'm just doing it in my head (and using ...1 to represent it) -- basically the smallest possible non-zero number.

Well I did say it doesn't make much sense didn't I? :D
I just invented (0.000...1) by subtracting (0.999...) from 1

In that case, what is 0.999...8 equal to? i.e. an infinite number of 9's with an 8 at the end. That probably doesn't make much sense mathematically and maybe even logically, but then again, if...

Oh that's right! So in that case:

sqrt( 1 ) = sqrt( -1 ) * sqrt( -1 ) = (+i) * (-i) = 1
Problem fixed. :)

sqrt(-1) = i
i * i = -1[/QUOTE]

Actually, the first one is right (look at the parenthesis):
sqrt( (-1) * (-1) ) = sqrt( 1 ) = 1

The second one is where reality flies out the window since it...